Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.3 - Double-Angle, Power-Reducing, and Half-Angle Formulas - Concept and Vocabulary Check - Page 679: 3


The required value of the tan 2B is $\frac{2\tan \,B}{1-{{\tan }^{2}}B}$.

Work Step by Step

In order to find the value of tan 2B, the double angle formula is used: $\tan \left( \alpha +\beta \right)=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }$ Now, consider $\alpha $ and $\beta $ as B; then the formula becomes: $\begin{align} & \tan \left( B+B \right)=\frac{\tan B+\tan \,B}{1-\tan B\tan B} \\ & =\frac{2\tan \,B}{1-{{\tan }^{2}}B} \end{align}$ Hence, the required value of tan 2B is $\frac{2\tan \,B}{1-{{\tan }^{2}}B}$.
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